Transcript Lecture 2: Overview of Computer Simulation of Biological

Lecture 2: Overview of Computer Simulation of Biological
Pathways and Network Crosstalk
Y.Z. Chen
Department of Pharmacy
National University of Singapore
Tel: 65-6616-6877; Email: [email protected] ; Web: http://bidd.nus.edu.sg
Content
•
Biological pathways and crosstalk
•
Simulation model development
•
Example: Development of simulation model of RhoA crosstalk
to EGFR-ERK pathways
•
Future perspectives: more pathways, more crosstalk, network
level drug effects, signaling specificity, component sensitivity,
TCM mechanism
Generic Signaling Pathway
Signal
Receptor
(sensor)
Transduction
Cascade
Targets
Metabolic
Enzyme
Response
Altered
Metabolism
Gene Regulator
Altered
Gene
Expression
Cytoskeletal Protein
Altered Cell
Shape or
Motility
Integrated
circuit of the cell
EGFRERK/MAPK
Signaling
Pathways
Crosstalk
of Rho
and Ras
The Multiple Functions of Rho
Aznar & Lacal Cancer Lett 165, 1 (2001)
Hall Biochem Society Transactions 33, 891 (2005)
Actin Cytoskeleton Regulation Pathways
KEGG database
Crosstalk between RhoA and EGFRERK/MAPK via MEKK1 and PTEN
• RhoA promotes ERK activation by its interaction with Rho kinase, an
effector of RhoA, which helps to delay EGF receptor endocytosis by
phosphorylating endophilin A1 and to prevent Akt inhibition of Raf by
activating phosphatase PTEN that hydrolyzes Akt second messenger
PIP3.
• RhoA binds to MEKK1 and activate its kinase activity which
subsequently phosphorylates and activates MEK1
• As activated MEK1 promotes ERK activation, it is of interest to
examine to what extent RhoA can prolong ERK/MAPK activity via this
MEKK1-mediated crosstalk between RhoA and EGFR-ERK signaling
networks
Gallagher et al. J Biol Chem 2004: 279, 1872
RhoA's crosstalk to EGFR-mediated Ras/MAPK
activation via MEKK1
RhoA's crosstalk to EGFR-mediated Ras/MAPK
activation via PTEN
Pathway Mathematical Model
•
Biochemical kinetics based on mass action law (Guldberg
and Waage 1864)
Fussenegger et al Nature Biotech 18, 768 (2000)
Schoeberl et al Nature Biotech 20, 370 (2002)
Sasagawa et al Nature Cell Biol 7, 365 (2005)
Kiyatkin et al J Biol Chem 281, 19925 (2006)
S1  S 2 
 P1  P2
Pathway Mathematical Model
•
Biochemical kinetics based on mass action law (Guldberg
and Waage 1864)
S1  S 2 
 P1  P2
Fussenegger et al Nature Biotech 18, 768 (2000)
Schoeberl et al Nature Biotech 20, 370 (2002)
Sasagawa et al Nature Cell Biol 7, 365 (2005)
Kiyatkin et al J Biol Chem 281, 19925 (2006)
Pathway Mathematical Model
•
Michaelis-Menton Kinetics (Leonor Michaelis 1875-1947;
Maud Menton 1879-1960)
• The rate of the reaction is equal to the negative rate of
decay of the substate as well as the rate of product
formation
S2
 P1  P2
•
Initial concentration of the substrate is much larger than the
concentration of the enzyme
•
Leading to:
Pathway Mathematical Model
S2
 P1  P2
Materi & Wishart
Drug Discov Today 12, 295 (2007)
Pathway Mathematical Model
S2
 P1  P2
Alderidge et al.
Nature Cell Biol 8, 1195 (2006)
Pathway Mathematical Model
S2
 P1  P2
Alderidge et al.
Nature Cell Biol
8, 1195 (2006)
Pathway Mathematical Model
S2
 P1  P2
Alderidge et al.
Nature Cell Biol 8, 1195 (2006)
Solving the Pathway Equations
Runge-Kutta method
• Our task is to solve the differential equation: dx/dt = f(t, y), x(t0)= x0
• Clearly, the most obvious scheme to solve the above equation is to
replace the differentials by finite differences:
dt = h
dx = x(t+h) - x(t)
• One can then apply the Euler method or first-order Runge-Kutta formula:
x(t+h) = x(t) + h f(t, x(t)) + O(h2)
• The term first order refers to the fact that the equation is accurate to first
order in the small step size h, thus the (local) truncation error is of order
h2. The Euler method is not recommended for practical use, because it is
less accurate in comparison to other methods and it is not very stable.
Solving the Pathway Equations
Runge-Kutta method
• The accuracy of the approximation can be improved by evaluating the
function f at two points, once at the starting point, and once at the
midpoint. This lead to the second-order Runge-Kutta or midpoint method:
k1 = h f(t, x(t))
k2 = h f(t+h/2, x(t)+k1/2)
x(t + h) = x(t) + k2 + O(h3)
• The most popular Runge-Kutta formula is the fourth-order one:
k1 = h f(t, x(t))
k2 = h f(t+h/2, x(t)+k1/2)
k3 = h f(t+h/2, x(t)+k2/2)
k4 = h f(t+h, x(t)+k3)
x(t + h) = x(t) + k1/6 + k2/3 + k3/3 + k4/6 + O(h5)
Solving the Pathway Equations
Cash-Karp embedded Runge-Kutta algorithm
Mathematical Model of
EGFR-ERK/MAPK Pathway
•
S1  S 2 
 P1  P2
Interaction equations and kinetic parameters
Mathematical Model of
EGFR-ERK/MAPK Pathway
•
S1  S 2 
 P1  P2
Interaction equations and kinetic parameters
Mathematical Model of
EGFR-ERK/MAPK Pathway
•
S1  S 2 
 P1  P2
Analysis of kinetic parameters
Mathematical Model of
EGFR-ERK/MAPK Pathway
•
S1  S 2 
 P1  P2
Analysis of kinetic parameters
Mathematical Model of
EGFR-ERK/MAPK Pathway
•
S1  S 2 
 P1  P2
Analysis of kinetic parameters
Validation of RhoA EGFR-ERK/MAPK
Crosstalk Model
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Time-dependent behavior of EGF activation of ERK in PC12 cells
• Our model predicted that ERK activation peaks at ~5 minutes
and decays within ~50 minutes, in good agreement with
observation
S1  S 2 
 P1  P2
Validation of RhoA EGFR-ERK/MAPK
Crosstalk Model
•
EGF variation on duration of ERK activation in PC12 cells
• Our model predicted that further increase of EGF levels leads
to sustained ERK activation, in good agreement with
observation and previous simulation results
S1  S 2 
 P1  P2
Validation of RhoA EGFR-ERK/MAPK
Crosstalk Model
•
Time-dependent behavior of active RasGTP and their effects on
ERK activation in PC12 cells
• Our model predicted that RasGTP peaks at ~2.5 minutes and
quickly decays to its basal levels within 20 minutes, in good
agreement with observation and previous simulation results
S1  S 2 
 P1  P2
Validation of RhoA EGFR-ERK/MAPK
Crosstalk Model
•
Time-dependent behavior of active RasGTP and their effects on
ERK activation in PC12 cells
• Our model predicted that Ras over-expression prolongs ERK
activation by delaying its decay rate without altering the time
cause for reaching the peak of activation, in good agreement
with observation and previous simulation results
S1  S 2 
 P1  P2
Validation of RhoA EGFR-ERK/MAPK
Crosstalk Model
•
Effect of scaffold protein MEKK1 on ERK activities
• Our model predicted that Increased MEKK1 concentration
helps to increase the level of active ERK, delay its peak time,
and slightly prolong the duration of ERK activation, in good
agreement with observation
S1  S 2 
 P1  P2
Validation of RhoA EGFR-ERK/MAPK
Crosstalk Model
•
Effects of Ras over-expression on RhoA and ERK activities
• Our model predicted that Ras over-expression increases the
amount of active GTP-bound RhoA and prolongs the duration
of its activation, leads to sustained ERK activation, in good
agreement with observation and previous simulation results
S1  S 2 
 P1  P2
Effects of RhoA over-expression on ERK
activation
•
When Ras expression is at the normal level, RhoA overexpression was found to prolong ERK activation in a dosedependent manner
S1  S 2 
 P1  P2
Effects of RhoA over-expression on ERK
activation
•
Effect of scaffold
S1  S 2 
 P1  P2
Effects of RhoA over-expression on ERK
activation
•
When Ras is over-expressed, RhoA over-expression significantly
reduces the number of active ERK while further prolonging its
activation
S1  S 2 
 P1  P2
Future Work: Other Pathways
KEGG database
Pathways and Disease
•
Mapping normal and cancer cell signalling networks: towards
single-cell proteomics Nature Rev Cancer 6, 146, 2006
P
Future
Trend:
More
crosstalk
e.g. crosstalk of
EGFR-ERK
pathway to
others via RTK
- PI3K – AKT
pathways
Future
Trend:
P
Network
level drug
effects
e.g. drug
combinations
in RTK-ERK
and RTK PI3K – AKT
pathways
Annals Oncology 18, 421 (2007)
Drug metabolism pathway simulation
published in PloS Comput Biol 3, e55 (2007)
Future
Trend:
Knowledge
learned
and
information
gained be
used for
studying
TCM
Project Assignment
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Project 1: Development of pathway simulation models
•
•
You will be given a section of a biological pathway. You
are required to try to generate a more detailed and
precise pathway section, derive the corresponding
pathway equations and parameters, and implement the
equations in an ODE solver
Project 2: Mechanism of biological crosstalks
•
You will be given a few papers of crosstalks between
different biological entities. You are required to probe
the mechanism of each of these crosstalks based on their
network relationships (generated by Pathway studio),
expression profiles (generated by microarray analysis),
and biochemical or regulatory profiles (from literature
reports)